Study of structure transition and crystallization of amorphous silica under compression

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In this work, we use molecular dynamic (MD) simulation to study the structure transition and crystallization of amorphous silica (SiO2) under compression. The structural evolution of amorphous SiO2 is explained through radial distribution function, coordination number distribution, bond angle distribution and visualization.

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Nội dung Text: Study of structure transition and crystallization of amorphous silica under compression

VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 Original Article Study of Structure Transition and Crystallization of Amorphous Silica under Compression Giap Thi Thuy Trang1,2, Pham Huu Kien1,* 1 Thai Nguyen University of Education, 20 Luong Ngoc Quyen, Thai Nguyen, Vietnam 2 Ha Noi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam Received 29 October 2019 Revised 13 December 2019; Accepted 25 December 2019 Abstract: In this work, we use molecular dynamic (MD) simulation to study the structure transition and crystallization of amorphous silica (SiO2) under compression. The structural evolution of amorphous SiO2 is explained through radial distribution function, coordination number distribution, bond angle distribution and visualization. Simulation result shown that there is a structural transformation from tetrahedral to octahedral network through SiO 5 units. In the 5- 15 GPa pressure range, structural transformation occurs powerfully and there are three structural phases corresponding to SiO4-, SiO5-, and SiO6- ones. At 15 GPa, octahedral-network (SiO6) is dominant. It is the first time we showed that when pressure is higher than 20 GPa, octahedral- network of amorphous SiO2 has a tendency to transform to stishovite crystalline phase. Keywords: Compression, crystallization, structural transformation, phase, amorphous. 1. Introduction Structural phase transformation under pressure of SiO2 is interesting that it is great importance in technology and geophysics [1-5]. The wide range distribution of Si-O-Si bond angle and bond length in silica gives rise to a rich variety of structures of phases in this system as functions of pressure and temperature. The laxity of the structure is the important condition of existence of the glass state. It accounts for the specific glass-forming properties of SiO2 and for the very low ability of forming crystalline of amorphous silica. The behavior of various high pressure silica phases has been investigated by both theory and experiment for a long time [6-10]. For instance, using the first- principles 29Si NMR analysis, Mauri et al. [11] reported that the structural transformations at low- ________ Corresponding author. Email address: phamhuukien@dhsptn.edu.vn https//doi.org/ 10.25073/2588-1124/vnumap.4422 13
14 G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 pressure are only accompanied by changes Si-O-Si bond angle without the change in local structure of Si. The coordination change from SiO4 to SiO6 is only observed experimentally at pressures beyond 8 GPa (700 K) by the formation of stishovite. Using MD simulation, Teter et al. [6] also reported that at pressure beyond 50 GPa, stishovite transforms to a phase having the CaCl2 structure type, which also contains SiO6. Increases in Si coordination have also been observed from spectroscopic and diffraction measurements of statically compressed silica glass/quartz at room temperature. Using MD simulations with an ab initio parameterized potential, Liu et al. [12] revealed the transformation pathways leading to a high pressure octahedral (HPO) phase. HPO phase has an O atoms hcp sub-lattice featuring and some point defects. They also showed that the HPO phase formed via a continuous rearrangement of the hcp sub-lattice. Meanwhile, the high pressure amorphous phases were described by an fcc and hcp sub-lattice mixture. Based on X-ray diffraction and ab initio simulations, Bykova et al. [13] suggested that SiO2 liquid in Earth’s lower mantle has complex structures making them more compressible than previously supposed. S. Petitgirard et al. [14] has used X-ray Raman scattering spectroscopy and MD simulations to study of SiO2 melts. They found that coordination higher than 6 is only reached beyond 140 GPa, corroborating results from Brillouin scattering. Network modifying elements in SiO 2 melts may shift this change in coordination to lower pressures and thus magmas could be denser than residual solids at the depth of the core-mantle boundary. Wu et al. [15] used x-ray Raman scattering (XRS), Brillouin scattering and diffraction to study on SiO2 glass. They found that the origin of the ‘two peaks’ pattern in the XRS was found to be the result of increased packing of O near the Si atom. The compression mechanism connected the presence of 5- and 6-fold coordinated silicon. A slight increase in the Si-O coordination higher than 6 was found to accompany the increase in the acoustic wave velocity near pressure of 140 GPa. Most of the observed stable and metastable crystalline phases of silica consists of either SiO4 or SiO6 units [16, 17]. P.K. Hung et al. [19] has used MD simulations to investigate the a-quartz under nonhydrostatic stress found evidence for a crystalline phase of SiO2 composed entirely of SiO5 units. However, the network structure as well as the crystallization of amorphous silica under compression is still in debate. We just found a few the publishing about crystallization process of amorphous SiO2. Therefore in this work, we focused on considering the structure transition and crystallization of amorphous SiO2 at 450 K and in pressure range from 0 to 30 GPa via analysis of RDF, coordination number distribution, bond angle distribution, visualization, the characteristics and distribution of basic structural units SiO4, SiO5 and SiO6. 2. Computational Procedure The periodic boundary conditions and the van Beest, Kramer, van Santen (BKS) potential are adopted [18] because it is simple. It can produce amorphous silica models with structural properties, density and thermal expansion that is in good agreement with experimental data [19-23]. It had following formula: qi q j Cij U ij ( rij )   Aij e - Bij rij - rij rij6 (1) where, rij is the distance between two atoms i and j; qi and qj are the charges of i and j, qq  respectively; Aij, Bij and Cij are constants. In expression (1), the first term  i j  : describes the  r   ij 
G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 15   Coulomb interaction between ions. The second term Aij e- B r : describes the pushing interaction at a ij ij distance close to the dominant electronic-electronic interaction and appears as the atoms come so close  C  that their electronic clouds overlap each other. The last term:  - 6ij  describes the interaction at a  r   ij  close distance derived from the distribution of electrons in the atom that make up the dipole - dipole interaction. The BKS potential constants are determined by the optimization of the parameters in the simulation so that the calculation results are more empirical; This helps the model to be built based on the BKS potential close to the real system. The values of potential constants corresponding to the Si-O and O- O atom pairs are listed in Table 1; disregard the near interaction potential between Si-Si atomic pairs. Table 1. The parameters of BKS potential for SiO2 Pairs Aij (eV) Bij (Å-1 ) Cij (eV Å6) Charges (e) O-O 1388.773 2.760 175.0 qO = − 1.2 Si-O 18003.757 4.873 33.538 qSi = + 2.4 Si-Si 0.0 0.0 0.0 The BKS models have played a significant role in numerous works of silica and related materials in the area of Materials Science as well as Geophysics. Namely, the BKS models was used to build silica models in different states, for example amorphous [21-23], crystals [24, 25 ] and liquid silica [26, 27]. In ref. [24, 25] compared the silica crystal structure obtained from simulation using the BKS potential with empirical studies with similar results. In addition, in ref. [27] calculated microstructure and density with this interaction potential giving results close to the results obtained from the experiment. The BKS models also have been applied in studies of amorphization of quartz under compression [28], the structural phase transformation from α to β quartz [29, 30], the liquid-liquid phase transition in silica [31]. Although it produces well structural properties for silica and has been used widely, it exposes the quantitative deficiencies. Namely, in the work [32], the authors have shown that: the S-L-C triple point occurs at 13.4 GPa in real silica, but at only 5.8 GPa in the model. Generally, the pressure range of the crystal stability areas is significantly lower in the model. In spite of its quantitative deficiencies, the BKS model describes the silica systems at the molecular level quite well. The long-range Coulomb interactions are calculated with the standard Ewald summation technique. We used the Verlet algorithm to integrate the motion equation. MD time step is equal to 0.41 fs. The initial configuration is generated by placing all atoms randomly in a simulation box and heating it up to 5000 K to remove initial configuration. After that the model is cooled down from 5000 to 450 K. Then, a long relaxation has been done to get equilibrium state using NPT ensemble (in NPT ensemble, number of atoms (N), pressure (P) and temperature (T) are conserved). The structural data of considered models is determined by averaging over 1000 configurations during the last 5×105 time steps. 3. Results and Discussion Firstly, as we have known, the radial distribution function (RDF) allows determining the average number of atoms at any given atomic distance. The average coordination number, bond length and bond angle will also determine via the RDF. Figure 1 displays RDF of contracted models. For Si-O pair, we show that at zero pressure, the first peak of RDF is very sharp. This demonstrates that at low
16 G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 pressure, local structure in amorphous silica or short range order structure is more order. Position of this peak located in 1.60 Ǻ which is in good agreement with the data reported in the experiment and simulation works [19-20, 33]. At 5, 10, 15 and 20 GPa pressure, the height of the first peaks of RDF strongly decreases and position shifts to the right. This indicates that the short range order structure is slightly dependent on pressure and the Si-O bond length increases slightly with pressure. At 20, 30 GPa, the height of the first peak of RDF increases with pressure and the position shifts to the left. This indicates that beyond 20 GPa, the degree of short range order increases and the Si-O bond length decreases as pressure increases. We also show that beyond 20 GPa, the RDFs of Si-O pair have many peaks which indicate the formation of crystal structure. It can be explained that amorphous silica tends transforming to crystal structure under compression. For O-O pair, as can be seen that in the 0-30 GPa pressure range, the height of the first peak of RDFs of the O-O pair increases and its position shifts to left as pressure increases. It means that the O-O bond length decreases with the increase of pressure. Similar to Si-O RDF, O-O RDF has many peaks at pressure of 20, 30 GPa. For Si-Si pair, it can be seen that as pressure increases, the location of the first peak of Si-Si pair of RDF shifts to the left and the first peak is splitted into two small peaks at 20, 30 GPa. At low pressure (0, 5 GPa), the Si-Si bond length is 3.10 At high pressure (10, 15, 20, 30 GPa), there are two Si-Si bond lengths, one at about 3.06 and another at about 2.64 Ǻ. Like to Si-O RDF and O-O RDF, Si-Si RDF also has many peaks at pressure 20, 30 GPa. This demonstrates one time again that the structure of SiO2 tends to form crystalline phases at high pressure (20, 30 GPa). From the above analysis, we can conclude that as under compression, the Si-O bond length increases while the Si-Si and O-O bond lengths decreases. This means that SiO2 solid transform from amorphous to crystalline phase. 9 gO-O(r) 6 3 0 21 0 GPa; 5 GPa; 15 GPa gSi-O(r) 14 15 GPa; 20 GPa; 20 GPa 7 0 9 gSi-Si(r) 6 3 0 0 2 4 6 8 r (angstrom) Figure 1. Radial distribution functions (RDF) g(r) of models for Si-Si, Si-O and O-O pairs at 450 K and different pressure. Next, we will clarify the origin of the change of Si-O, O-O and Si-Si bond lengths under compression. Figure 2, we can see that as pressure increases, there is a transformation in local environment of Si ions from tetrahedral- to octahedral- coordination. This can be consequences the decrease of O-Si-O bond angle. As can see Figure 3, the O-Si-O bond angle in SiO5 units is smaller than the one in SiO4 and larger than the one in SiO6 units. Therefore, the bond length between O and O ions in SiO5 units is smaller than the one in SiO4 and larger than the one in SiO6. It means that the increase of Si-O coordination number lead to the decrease of O-O bond length. This result in increasing the Coulomb repulsion between O-- and O-- ions and the increase of Coulomb repulsion
G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 17 leads to elongation of the Si-O bond length. In the 0-20 GPa pressure range, the increase of coordination of Si with pressure will lead to the increase of Si-O bond length. At 20 GPa, most of Si has octahedral coordination (as can see Figure 2a). In the 20-30 GPa pressure range, the increase of pressure will not lead to the increase of the Si-O bond length but lead to the decrease of the Si-O bond length (see Figure 1). For the Si-Si pair, the increase of pressure will result in the decrease of Si-Si bond length and the splitting of the first peak of Si-Si pair RDF. It can be explained as following, the increase of pressure will lead to increasing coordination number of O atoms. At low pressure (0, 5, 10 GPa) most of O is surrounded by two Si atoms while at high pressure (>10 GPa), most of O is surrounded by three Si atoms (as can see Figure 2b). The increase of the coordination number consequences in the decrease of Si-O-Si bond angle as can be seen in Figure 4. At low pressure, most of the Si-O-Si is around 140-145o. At high pressure, the Si-O-Si bond angle distribution has two peaks. For OSi2 linkage, the peaks locate at 1050 and 1430. For OSi3 linkage, the peaks locate at 950 and 1300. The decrease of Si-O-Si angle leads to the decrease of Si-Si bond length. This result in increasing the Coulomb repulsion and it one again leads to elongation of the Si-O bond length. The distribution of Si-O-Si has two peaks this result in forming two Si- Si bond distances. The Si-Si bond distance of 3.06 and 2.64 Ǻ corresponds to two peaks of Si-O-Si bond angle distribution. Comparing to Si-O-Si and O-Si-O angles for amorphous SiO2 as can be seen in Figure 5, we show that bond angle distributions in SiO4, SiO5 and SiO6 units are quite close to Si-O-Si and O-Si-O angles at low and high pressure. This also means that at high pressure, the structure of SiO2 solid has stishovite crystal. Figure 2. The coordination number distribution as a function of pressure: a) Si surrounds O; b) O surrounds Si. Figure 3. The O-Si-O bond angle distribution in SiO4, SiO5 and SiO6 units at different pressure.
18 G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 Figure 4. The Si-O-Si bond angle distribution under pressure. Figure 5. Schematics of basic structure units of amorphous SiO2 at low (a) and high (b) pressure. A clear structural change that shows the phase transformation from tetrahedral to octahedral structure (stishovite crystal) as pressure increases. It can be seen that Si-O-Si and O-Si-O angles are equal to 130o, 109o for low model and 90o, 90o for high model, respectively. Finally, we use visualization to study atom arrangement distribution in amorphous SiO2. Figure 6 displays the snapshot of the atom arrangement distribution in the amorphous SiO2 at 0 GPa and 30 GPa. It can be seen that at high pressure, atom arrangement is more order than ones at low pressure. This again demonstrates that the crystallization has occurred at high pressure. We will also display the modification number of structural units SiO6 in amorphous SiO2 system using 3D visualization. As we can see on Figure 7, the order degree of SiO6 units depends on pressure. At 30 GPa, most of structural units are SiO6 and they tend to form crystalline phase. Number of structural units SiO6 at 0 GPs is much less than ones at 30 GPa. Figure 7 also demonstrates that the structural units SiO6 form crystalline regions with different crystalline directions in model. In order to show more clearly, we visualize the spatial distribution of SiO4, SiO5 and SiO6 in the amorphous SiO2 at pressure of 0, 10, 20 and 30 GPa. It can be seen in Figure 8, the distribution of coordination SiOx units is not uniform but it tends to forms separated clusters (subnets) of SiO4, SiO5 and SiO6.
G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 19 Figure 6. Snapshot of the atom arrangement distribution in the amorphous SiO2 at 0 GPa (left) 30 GPa (right): the red (large) sphere presents Si atom, the blue (small) sphere presents O atom. A B Figure 7. (A) Snapshot of the spattial distribution of SiO6 in the amorphous SiO2 at 0 GPa (left) 30 GPa (right): the red sphere presents Si atom, the blue sphere presents O atom. (B) The structure of stishovite crystalline (left) and the model of amorphous SiO2 that is compressed at 30 GPa (right)
20 G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 It means that the structure of amorphous SiO2 comprises the mixture of SiO4, SiO5 and SiO6 clusters. Namely, the structure of SiO2 is the mixture of regions with different short range order. From the structural difference amongst regions, we can see that the structure of SiO 2 consists of structural phases is that SiO4-, SiO5- and SiO6-phases, where SiOx (x=4,5,6) phases are the phase formed by SiOx units, respectively. It can be seen that at low pressure (0 GPa), the regions with SiO 4-phase are linked each to other forming a large region with the expanse almost whole model. The regions with SiO5- and SiO6-phases are small and localized at different locations forming separated regions. As pressure increases, the regions with SiO5-and SiO6-phases are expanded and the regions with SiO4-phase are shrunk. At pressure of 30 GPa, the regions with SiO4- and SiO5-phases are shrunk, whereas the regions with SiO6-phase are expanded almost the whole model. Especially, at pressure of 30 GPa, the structure of SiO2 is SiO6-phase with the high order degree (long order structure) and they tend to transformation into crystal structure, namely it is stishovite crystal as above analyzed. Figure 8. Spatial distribution of SiO4, SiO5 and SiO6 in the amorphous SiO2 at pressure of 0, 15, 20 and 40 GPa: Here A1), B1)… D1) are SiO4 units; SiO5 and SiO6 units are A2), B2)… D2) and A2), B3)… D3), respectively; Si and O atoms are in red and blue ball, respectively.
G.T.T. Trang, P.H. Kien / VNU Journal of Science: Mathematics – Physics, Vol. 36, No. 2 (2020) 13-22 21 4. Conclusion The structure transition and crystallization of amorphous silica under compression have been investigated. Several results are demonstrated as follows (i) There is a structural transformation from tetrahedral- to octahedral- network through SiO5 units. In the 5-15 GPa pressure range, structural transformation occurs strongly and there are three structural phases corresponding to SiO4-, SiO5-, and SiO6 ones. (ii) At 15 GPa, octahedral-network is dominant. When pressure is higher than 20 GPa, octahedral-network tends to transform to stishovite crystalline phase. Namely, the structural units SiO 6 form stishovite crystalline regions with different crystalline directions in model. However, the crystalline mechanism in amorphous SiO2 will be focused on the next researchs. Acknowledgements This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.02-2018.312. This work was supported by the Domestic Master/PhD Scholarship Programme of Vingroup Innovation Foundation under grant number VINIF.2019.TS.70 References [1] A.R. Oganov, M.J. Gillan, G.D. Price, Structural stability of silica at high pressures and temperatures, Physical Review B 71 (2010) 064104. [2] V.P. Prakapenka, Guoyin Shen, L.S. Dubrovinsky, M.L. Rivers, S.R. Sutton, High pressure induced phase transformation of SiO2 and GeO2 : difference and similarity, Journal of Physics and Chemistry of Solids 65 (2004) 1537-1545. [3] K.J. Kingma, R.E. Cohen, R.J. Hemley, H.K. Mao, Transformation of stishovite to a denser phase at lower- mantle pressures, Nature 374 (1995) 243-245. [4] S.R. Shieh, T.S. Duffy, B. Li, Strength and Elasticity of SiO2 across the Stishovite–CaCl2-type Structural Phase Boundary, Physical Review Letters 89 (2002) 255507. [5] S. Ono, K. Hirose, M. Murakami, M. Isshiki, Post-stishovite phase boundary in SiO2 determined by in situ X-ray observations, Earth and Planetary Science Letters 197 (2002) 187-192. [6] D.M. Teter, R.J. Hemley, G. Kresse, J. Hafner, High pressure polymorphism in silica, Physical Review Letters 80 (1998) 2145-2148. [7] L.S. Dubrovinsky, N.A. Dubrovinskaya, S.K. Saxena, F. Tutti, S. Rekhi, T.L. Bihan, G. Shen, J. Hu, Pressure- induced transformations of cristobalite, Chemical Physics Letters 333 (2001) 264-270. [8] D. Andrault, G. Fiquet, F. Guyot, M. Hanfland, Pressure-induced Landau-type transition in stishovite, Science 282 (1998) 720-724. [9] D. Andrault, R.J. Angel, J.L. Mosenfelder, T.L. Bihan, Equation of state of stishovite to lower mantle pressures, American Mineralogist 88 (2003) 301-307. [10] L.T. San, N.V. Hong, P.K. Hung, Polyamorphism of liquid silica under compression based on five order- parameters and two-state model: a completed and unified description, High Pressure Research 36 (2016) 187- 197. [11] F. Mauri et al., Si-O-Si bond-angle distribution in vitreous silica from first-principles 29Si NMR analysis, Physical Review B 62 (2000) R4786. [12] Wei Liu et al., Multiple pathways in pressure-induced phase transition of coesite, Proceedings of the National Academy of Sciences 114 (2017) 12894-12899.
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